Jim Lou is correct.
There are three steps to an electrical connection.
1. Mechanical connection.
That would be the crimp connectors, or twisting the wires together.
Don't be fooled into thinking this is an electrical connection or you will be fixing things until the cows come home...
2. Electrical connection.
Silver bearing solder (Radio Shack p/n 64-013 is a fine example) is the way to go.
Never use acid core solder on electrical components.
The Radio Shack 2% silver solder is very good for electrical connections and sticks to damn near everything.
3. Insulation & Environmental protection.
I like to use a heat shrink tubing with 'Glue' in it.
(The 'Goo' Jim Lou was talking about)
The vinyl crap sold at Radio Shack is no good, you will have to hunt for good heat shrink tubing.
Jim Lou's idea about the Liquid Electrical Tape then heat shrink tubing makes sense to me.
There are crimp connectors with solder and heat shrink tubing already attached to them. Not real common, but worth the hunt.
Crimp, then when you use the heat gun to shrink the tubing, the solder melts into the joint.
Shrink and solder in one step. Saves fingers from the soldering iron too!
How they get the solder to go liquid at that low of a temp is beyond me.
When you get wire, use virgin copper wire.
Alloy wire (usually a dull color, not bright like copper should be) will corrode no matter what you do, be hard to solder, and is generally more trouble than it's worth.